Determination of tissue oxygen saturation by diffuse reflectance spectroscopy

Abstract. Significance Tissue oxygenation is a parameter that allows for determining the health status of human beings. In diabetic patients, it is particularly important to evaluate this parameter as an indicator of microcirculatory problems in the extremities. Aim We aim to obtain tissue oxygen saturation from diffuse reflectance measurements. Approach A computational algorithm to automate the methodology was implemented with the aim of establishing a medical diagnosis technique that is non-invasive and easy to apply and requires a short evaluation time. Tissue oxygen saturation measurements were performed on a group of volunteers to whom a vascular occlusion was applied. It was observed that, by increasing the applied pressure to the arm of each volunteer, the tissue oxygen saturation progressively decreased. Results The results indicate that the developed technique is an effective method for monitoring changes in blood hemodynamics in patients with some type of pathology in which tissue oxygenation is compromised. In addition, the expected behavior of tissue oxygen saturation during a vascular occlusion was obtained. Conclusions A methodology to obtain tissue oxygen saturation from diffuse reflectance measurements was successfully developed. It meets the necessary characteristics to be considered a technique for obtaining StO2 because it can be applied in vivo and non-invasively and does not require a high computational cost; thus it is fast and capable of providing an objective and quantifiable evaluation.

According to Karsten and Smit [27] the absorption coefficient of human skin is proportional to the melanin content, that is, its skin type.
A diffuse reflection spectrum was measured on the palm of the hand for each volunteer and its absorption spectrum was calculated, following the methodology described by Quistián [23].In figure S1, the wavelength of 632 nm was chosen to show a comparison between the different skin types.The skin type label was obtained from a questionnaire based on the Fitzpatrick criteria.

II. Statistical analysis of the volunteers number
To perform the experimental tests, it is necessary to consider an appropriate sample size, since considering a very large sample size may imply a waste of resources and a very small size may lack practical use [41].Therefore, the number of volunteers() was obtained from equation S1, which indicates a relationship between the standard deviation (), reliability () and the desired confidence interval dimension (): where  depends on the confidence level (1 − ) and  represents the significance level.For example, for a value of  = 0.01 the confidence level is equal to 99% and its reliability will be  = 2.58, where  is obtained by matching the value of the confidence interval to ( √2 ⁄ ) with  the Gaussian error function.The value of  can be obtained from a preliminary sample ( 1 ) where a fitting is subsequently applied to the calculated sample size () and a number of observations needed to complete the total sample size requirement is obtained.(2 ), as indicated by equation S2: In this work, a confidence level of 95% was considered, which provides a value of  = 1.96, a confidence interval dimension  = 1 and a standard deviation  = 2.65 (obtained from a preliminary sample of 64 measurements with 16 volunteers as shown in table S1).The volunteers number obtained was compared with other studies that also applied a vascular occlusion test to healthy volunteers.Table S2 shows the review of the volunteers number that were used in mentioned studies, where it can be seen that the number of volunteers that we consider in this work is within the reported range.

Principal Components Analysis
There are different chromophores present in the human skin (hemoglobin, melanin, water, etc.) these exhibit a characteristic absorption spectrum.Principal component analysis (PCA) can be applied to linearly transform data from an orthogonal coordinate system.This procedure indicates that the principal components corresponding to the axes of the system are determined as eigenvectors of the covariance matrix of the data set, and their corresponding eigenvalues refer to the variance captured within each eigenvector [46].
A PCA on the main chromophores of the skin was carried out (considering their respective absorption coefficients), degree of correlation between skin chromophores was evaluated, as can be seen from the table S3.The molar concentration of hemoglobin of 64,500 gr/mol was used and for the coefficients of the rest of the skin chromophores, a specific concentration was not used.The data used for the PCA were obtained from the references mentioned on Jacques & Prahl omlc page and the units were converted to mm -1 .The absorption coefficients of fat [47] and hemoglobin [29] were taken directly.For the water absorption coefficient [48], a 4th order polynomial fit was performed to identify the values between the wavelengths of interest (500-700 nm and 974 nm), while for the melanin absorption coefficient [31] were obtained from the fit equations S3 and S4, considering the power factor (m=3) and the melanosome volume fraction (  =0.87).

𝜇
, = (519 cm −1 ) ( The percentage variance corresponding to the eigenvalues was also evaluated, as it is shown in the table S4, as well as the matrix of the eigenvectors generated in the analysis (table S5).The graphs of figure S2 show that the chromophores with the greatest effect on the total absorption coefficient are oxygenated hemoglobin, deoxygenated hemoglobin, and melanin.Figure S2b shows that these three chromophores with the greatest contribution are also more related to each other, since these present a small angle between their eigenvectors.

Figure S2 .
Figure S2.Graphs obtained from principal components analysis: a) Scree Plot, and b) Loading Plot.

Table S1 .
Therefore, substituting these values in equation S1, a sample size is obtained:  = 26.97≈ 27 volunteers.Preliminary sample standard deviation for sample size calculation.The mean of the standard deviation is 2.65.

Table S2 .
Review of volunteers number in various studies.

Table S3 .
Correlation matrix between main skin chromophores.